Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
148 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Dic110 | C2 | semidirect |
| 3. C11×#683 | C2 | semidirect |
| 5. #11724888 | C2 | semidirect |
| 6. Dic11⋊Dic5 | C2 | semidirect |
| 21. C2×C5×D11 | Q8 | semidirect |
| 55. #683 | D11 | semidirect |
| 56. C5×C11 | C22⋊Q8 | semidirect |
| 60. C2×D11 | Dic10 | semidirect |
| 98. C11 | #4024 | semidirect |
| 112. C5 | #66949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic110 | 2 |
| C2×Dic5×D11 | 2 |
| C11×#683 | 2 |
| C5×(C2×D11)⋊C4 | 2 |
| #11724888 | 2 |
| Dic11⋊Dic5 | 2 |
| (C2×D11)⋊Dic5 | 2 |
| #66949 | 5 |
| #4024 | 11 |